After momentary attention as potential battery materials during the 1980s, sodium titanium disulphides, like the whole Na–Ti–S system, have only been investigated in a slapdash fashion. While they pop up in current reviews on the very subject time and again, little is known about their actual crystal-structural features and sodium-ion diffusion within them. Herein, we present a short summary of literature on the Na–Ti–S system, a new synthesis route to Na_0.5TiS₂-3R₁, and results of high-temperature X-ray and neutron diffractometry on this polytype, which is stable for medium sodium content. Based thereon, we propose a revision of the crystal structure reported in earlier literature (missed inversion symmetry). Analyses of framework topology, probability-density functions, and maps of the scattering-length density reconstructed using maximum-entropy methods (all derived from neutron diffraction) reveal a honeycomb-like conduction pattern with linear pathways between adjacent sodium positions; one-particle potentials indicate associated activation barriers of ca. 0.1 eV or less. These findings are complemented by elemental analyses and comments on the high-temperature polytype Na_0.9TiS₂-2H. Our study helps to get a grip on structural complexity in the intercalates Na_xTiS₂, caused by the interplay of layer stacking and Na–Ti–vacancy ordering, and provides first experimental results on pathways and barriers of sodium-ion migration.